The introduction of generative artificial intelligence (AI) into the education field, by introducing non-human actors, breaks down the binary subject structure of traditional educational legal relationships. This paper argues that the current education governance system, designed based on the teacher-student binary relationship, suffers from institutional mismatches in three aspects: attribution of responsibility, definition of rights, and recognition of academic norms. Through normative analysis and institutional comparison, and drawing on international governance experiences such as China's Education Law, Copyright Law, Personal Information Protection Law, and Data Security Law, this paper identifies three core dilemmas: First, AI-generated outputs lack the necessary justification dimension for "knowledge" in a legal and educational sense; second, the algorithmic process cannot meet the normative standards of legal reasoning; and third, the current tort liability framework struggles to trace damages back to attributable human subjects. To resolve these mismatches, this paper proposes defining generative AI legally as a regulated auxiliary entity, a functional intermediate category between a tool and a legal subject. This concept embodies three institutional principles: traceable responsibility, identifiable use, and labelable generation. This framework, without granting AI legal personhood, incorporates technological autonomy into a human-centered order of responsibility, providing a theoretically sound and operationally feasible institutional model for AI governance in the education sector.